Many models of dynamical systems rely on the notion of a state-to-action emission matrix and a state-to-state transition matrix such as the prominent Hidden Markov Model (HMM) [1]} (sec:model). The matrices' rows describe discrete distributions that are often sampled independently from a Dirichlet distribution. This however results in the states and actions to be categorical without particular ordering. We refer to the distribution over this kind of stochastic matrices as Standard Matrix Dirichlet (SMD) (sec:smd). It not only discards ordinal information, but also leads to a problem called label switching [2]}: the order-invariance of states complicates interpretability and evaluation with conventional classification metrics.
